An Application of Generalized Entropy Optimization Methods in Survival Data Analysis

Abstract

In this paper, survival data analysis is realized by applying Generalized Entropy Optimization Methods (GEOM). It is known that all statistical distributions can be obtained as distribution by choosing corresponding moment functions. However, Generalized Entropy Optimization Distributions (GEOD) in the form of distributions which are obtained on basis of Shannon measure and supplementary optimization with respect to characterizing moment functions, more exactly represent the given statistical data. For this reason, survival data analysis by GEOD acquires a new significance. In this research, the data of the life table for engine failure data (1980) is examined. The performances of GEOD are established by Chi-Square criteria, Root Mean Square Error (RMSE) criteria and Shannon entropy measure, Kullback-Leibler measure. Comparison of GEOD with each other in the different senses shows that along of these distributions (MinMaxEnt) 4 is better in the senses of Shannon measure and of Kullback-Leibler measure. It is showed that, (MinMaxEnt) 3 ( (MaxMaxEnt) 4 ) is more suitable for statistical data among (MinMaxEnt) m ,m=1,2,3,4 (MaxMaxEnt) m , m=1,2,3,4 . Moreover, (MinMaxEnt) 3 is better for statistical data than (MaxMaxEnt) 4 in the sense of RMSE criteria. According to obtained distribution (MinMaxEnt) 3 (MaxMaxEnt) 4 estimator of Probability Density Function f<sup style="margin-left:-8px;">^</sup> (t) , Cumulative Distribution Functio F<sup style="margin-left:-8px;">^</sup> (t) , Survival Function &Scirc;( t) and Hazard Rate &hcirc; ( t) are evaluated and graphically illustrated. The results are acquired by using statistical software MATLAB.